Question

Rezolvati in R ecuatia: ㏒₃($x^{2} -16$ ) = 2. Vreau pas cu pas, va rog.

Answer 1

$\rm log_a b=c \rightarrow a^c=b \\ \\log_3 (x^2-16)=2 \\ \\ Deci~x^2-16=3^2 \\ \\ x^2-16=9 \\ \\ x^2-16-9=0 \\ \\ x^2-25=0 \\ \\ a^2-b^2=(a+b)(a-b) \rightarrow x^2-25=(x+5)(x-5) \\ \\ (x+5)(x-5)=0 \\ \\ I.x-5=0 \rightarrow \boxed{x=5} \\ II.x+5=0 \rightarrow \boxed{x=-5}$

Answer 2

㏒₃( x² - 16) = 2
x² -16 = 3²
x² - 16 = 9
x² = 9 + 16
x² = 25
x₁ = +√25= + 5
x₂ = - √25= - 5